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WASHINGTON, Sept. 18 — After rising for three straight weeks, new claims for unemployment benefits dropped last week to the lowest level in nearly a month, raising hopes that the pace of layoffs may be starting to slow down again.

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THE LABOR DEPARTMENT reported Thursday that for the work week ending Sept. 13, new claims for jobless benefits fell by a seasonally adjusted 29,000 to 399,000. In another somewhat encouraging note, the sharp decline pushed claims just below 400,000, a level associated with a weak labor market.

Last week’s level of claims was not only the lowest since the week ending Aug. 23 but also marked the first time since then that claims dipped below the 400,000 mark. The latest snapshot of the labor markets was slightly better than economists were expecting; they were forecasting claims to fall no lower than 410,000 for last week.

The more stable four-week moving average of claims, which smooths out week to week fluctuations, however, rose last week to 410,750, an increase of 2,000 from the previous week, and the highest level since the middle of July.

Although other parts of the economy are improving, the labor market is expected to be the last to heal. Economists believe companies will want to wait until profits get stronger and they have more confidence in the rebound’s vigor before they go a hiring spree.

The nation’s unemployment rate dipped to 6.1 percent in August, but businesses slashed 93,000 jobs, the seventh month in a row of job losses, a discouraging climate for jobseekers. Healthy productivity gains, meanwhile, has allowed companies to produce more with fewer workers, a factor contributing to the lackluster job situation, Federal Reserve Chairman Alan Greenspan says.

Greenspan and his Federal Open Market Committee colleagues on Tuesday decided to hold a key short-term interest rate at a 45-year low of 1 percent.

Fed policy-makers said economic data since the last meeting, on Aug. 12, confirmed that “spending is firming, although the labor market has been weakening.” That marked a slightly more cautious note on the jobs front from the August meeting when policy-makers said “labor market indicators are mixed.”

The number of unemployed Americans collecting jobless benefits for more than a week rose by 39,000 to 3.7 million for the work week ending Sept. 6, the most recent period for which that information was available.

Analysts expect the economy to pick up speed in the second half of this year, with estimates for growth ranging from rate of just over 4 percent to around a 5 percent pace. Some economists believe that by the end of the year, businesses will begin to step up hiring. Others don’t think that will happen until next year.

Were the job market to deteriorate and threaten the recovery, however, the Fed wouldn’t hesitate to cut its key short-term rate, economists said. Chances of that, however, are probably slim, they said.